If the inverse of is already known, the formula provides a numericallycheap way to compute the inverse of corrected by the matrix (depending on the point of view, the correction may be seen as a perturbation or as a rank-1 update). The computation is relatively cheap because the inverse of does not have to be computed from scratch (which in general is expensive), but can be computed by correcting (or perturbing) .

Using unit columns (columns from the identity matrix) for or , individual columns or rows of may be manipulated and a correspondingly updated inverse computed relatively cheaply in this way.[6] In the general case, where is a times matrix and and are arbitrary vectors of dimension , the whole matrix is updated[5] and the computation takes scalar multiplications.[7] If is a unit column, the computation takes only scalar multiplications. The same goes if is a unit column. If both and are unit columns, the computation takes only scalar multiplications.

^Sherman, Jack; Morrison, Winifred J. (1949). "Adjustment of an Inverse Matrix Corresponding to Changes in the Elements of a Given Column or a Given Row of the Original Matrix (abstract)". Annals of Mathematical Statistics20: 621. doi:10.1214/aoms/1177729959.